We present a graphical model framework for decoding in the visual ERP-based speller system. The proposed framework allows researchers to build generative models from which the decoding rules are obtained in a straightforward manner. We suggest two models for generating brain signals conditioned on the stimulus events. Both models incorporate letter frequency information but assume different dependencies between brain signals and stimulus events. For both models, we derive decoding rules and perform a discriminative training. We show on real visual speller data how decoding performance improves by incorporating letter frequency information and using a more realistic graphical model for the dependencies between the brain signals and the stimulus events. Furthermore, we discuss how the standard approach to decoding can be seen as a special case of the graphical model framework. The letter also gives more insight into the discriminative approach for decoding in the visual speller system.

From an information-theoretic perspective, a noisy transmission system such as a visual Brain-Computer Interface (BCI) speller could benefit from the use of errorcorrecting codes. However, optimizing the code solely according to the maximal minimum-Hamming-distance criterion tends to lead to an overall increase in target frequency of target stimuli, and hence a significantly reduced average
target-to-target interval (TTI), leading to difficulties in classifying the individual event-related potentials (ERPs) due to overlap and refractory effects. Clearly any change to the stimulus setup must also respect the possible psychophysiological consequences. Here we report new EEG data from experiments in which we explore stimulus types and codebooks in a within-subject design, finding an interaction between the two factors. Our data demonstrate that the traditional, rowcolumn code has particular spatial properties that lead to better performance than one would expect from its TTIs and Hamming-distances alone, but nonetheless error-correcting codes can improve performance provided the right stimulus type is used.

We reveal the presence of refractory and overlap effects in the event-related potentials in visual P300 speller datasets, and we show their negative impact on the performance of the system. This finding has important implications for how to encode the letters that can be selected for communication. However, we show that such effects are dependent on stimulus parameters: an alternative stimulus type based on apparent motion suffers less from the refractory effects and leads to an improved letter prediction performance.

For quantitative PET information, correction of tissue photon attenuation is mandatory. Generally in conventional PET, the attenuation map is obtained from a transmission scan, which uses a rotating radionuclide source, or from the CT scan in a combined PET/CT scanner. In the case of PET/MRI scanners currently under development, insufficient space for the rotating source exists; the attenuation map can be calculated from the MR image instead. This task is challenging because MR intensities correlate with proton densities and tissue-relaxation properties, rather than with attenuation-related mass density. METHODS: We used a combination of local pattern recognition and atlas registration, which captures global variation of anatomy, to predict pseudo-CT images from a given MR image. These pseudo-CT images were then used for attenuation correction, as the process would be performed in a PET/CT scanner. RESULTS: For human brain scans, we show on a database of 17 MR/CT image pairs that our method reliably enables e
stimation of a pseudo-CT image from the MR image alone. On additional datasets of MRI/PET/CT triplets of human brain scans, we compare MRI-based attenuation correction with CT-based correction. Our approach enables PET quantification with a mean error of 3.2% for predefined regions of interest, which we found to be clinically not significant. However, our method is not specific to brain imaging, and we show promising initial results on 1 whole-body animal dataset. CONCLUSION: This method allows reliable MRI-based attenuation correction for human brain scans. Further work is necessary to validate the method for whole-body imaging.

Kernel based nonlinear Feature Extraction (KFE) or dimensionality reduction is a widely used pre-processing step in pattern classification and data mining tasks. Given a positive definite kernel function, it is well known that the input data are implicitly mapped to a feature space with usually very high dimensionality. The goal of KFE is to find a low dimensional subspace of this feature space, which retains most of the information needed for classification or data analysis. In this paper, we propose a subspace kernel based on which the feature extraction problem is transformed to a kernel parameter learning problem. The key observation is that when projecting data into a low dimensional subspace of the feature space, the parameters that are used for describing this subspace can be regarded as the parameters of the kernel function between the projected data. Therefore current kernel parameter learning methods can be adapted to optimize this parameterized kernel function. Experimental results are provided to
validate the effectiveness of the proposed approach.

The Common Spatial Pattern (CSP) algorithm is a highly successful method for efficiently calculating spatial filters for brain signal classification. Spatial filtering can improve classification performance considerably, but demands that a large number of electrodes be mounted, which is inconvenient in day-to-day BCI usage. The CSP algorithm is also known for its tendency to overfit, i.e. to learn the noise in the training set rather than the signal. Both problems motivate an approach in which spatial filters are sparsified. We briefly sketch a reformulation of the problem which allows us to do this, using 1-norm regularisation. Focusing on the electrode selection issue, we present preliminary results on EEG data sets that suggest that effective spatial filters may be computed with as few as 10--20 electrodes, hence offering the potential to simplify the practical realisation of BCI systems significantly.

Given a spatial filtering algorithm that has allowed us to identify task-relevant EEG sources, we present a simple approach
for monitoring the activity of these sources while remaining relatively robust to changes in other (task-irrelevant) brain activity. The idea is to keep spatial *patterns* fixed rather than spatial filters, when transferring from
training to test sessions or from one time window to another. We show that a fixed spatial pattern (FSP)
approach, using a moving-window estimate of signal covariances, can be more robust to non-stationarity than a fixed spatial filter (FSF) approach.

We present easy-to-use alternatives to the often-used two-stage Common Spatial Pattern + classifier approach for spatial filtering and classification of Event-Related Desychnronization signals in BCI. We report two algorithms that aim to optimize the spatial filters according to a criterion more directly related to the ability of the algorithms to generalize to unseen data. Both are based upon the idea of treating the spatial filter coefficients as hyperparameters of a kernel or covariance function. We then optimize these hyper-parameters directly along side the normal classifier parameters with respect to our chosen learning objective function. The two objectives considered are margin maximization as used in Support-Vector Machines and the evidence maximization framework used in Gaussian Processes. Our experiments assessed generalization error as a function of the number of training points used, on 9 BCI competition data sets and 5 offline motor imagery data sets measured in Tubingen. Both our approaches sho
w consistent improvements relative to the commonly used CSP+linear classifier combination. Strikingly, the improvement is most significant in the higher noise cases, when either few trails are used for training, or with the most poorly performing subjects. This a reversal of the usual "rich get richer" effect in the development of CSP extensions, which tend to perform best when the signal is strong enough to accurately find their additional parameters. This makes our approach particularly suitable for clinical application where high levels of noise are to be expected.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems